Comedian Stewart (we loved him in “Elmopalooza!”) appeared on Fox’s “O’Reilly Factor” in a two-part interview broadcast Wednesday and Thursday nights. And he sparred with his host about national governance in a manner that would not have been out of place at a Brookings Institution seminar.

“This was pretty intellectual. I’m very, very pleased,” Mr. O’Reilly said when it was over.

But the pair started off with a fairly lengthy discussion about the nature of executive power, in which Stewart opined that President Obama had ceded too much by allowing Congress to draw up healthcare legislation on its own.

“Once you allow a vacuum of power, what will assume power in Washington is special interests,” Stewart said. “If you allow too much nitpicking on the edge of legislation, it will be necessarily turned into a type of lobbyist gruel.”

Then they moved to whether Mr. Obama is, or is not, a socialist.

“If he’s a tyrant, he’s a pretty tame tyrant,” Stewart said. “How many tyrants do you know of that suffer because they can’t get cloture?”

(He’s referring to the fact that Obama no longer has the votes to overcome a unified GOP filibuster in the Senate.)

Then O’Reilly said he was thinking of running for president in 2012, and he wanted to pick Stewart as his running mate, if they were compatible. The pair went issue by issue:

The war against terrorism. “Our strategy for battling terrorism can’t be that you overthrow governments, and then make the United States military commit 150,000 troops to those lands until they can be stabilized enough so you can prevent 10 people from plotting terrorism in a basement,” Stewart said.

“I agree.... It’s bankrupting the country,” O’Reilly said.

The trial of Khalid Sheikh Mohammed. Stewart sounded pretty tough on what he’d like to have happen to accused 9/11 mastermind Khalid Sheikh Mohammed.

“I’d like him executed at half time of the Super Bowl and then reanimated so we can do it every year,” he said.

The comedian disagreed with his host, however, who believes that trying KSM in civilian courts shows weakness.

“I understand the value of showing that the American justice system has the ability to handle even the worst,” Stewart said.

“I’m not a scientist. I can only assume common sense. If you burn a lot of stuff and put it in the atmosphere, it means something,” Stewart said.

Stewart and O’Reilly have appeared together many times and seemed more compatible on the issues than one might think. But it doesn’t take much to exceed expectations, since one would probably think that they weren’t compatible at all.

However, in the end Stewart did say, “I’m not running [for president] with you! I’d get one job, and that would be to light the White House menorah.”